Categorifications from planar diagrammatics

Abstract

A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive halves of quantum groups. These notes are a write-up of Takagi lectures given by the author in Hokkaido University in June 2009.

30 pages, latex, eps

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Cited by in corpus (19)

• Colored HOMFLY polynomials of knots presented as double fat diagrams
• Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
• Towards effective topological field theory for knots
• Colored knot polynomials. HOMFLY in representation [2,1]
• Knot invariants from Virasoro related representation and pretzel knots
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Higher-Dimensional Algebra VII: Groupoidification
• An introduction to diagrammatic algebra and categorified quantum sl(2)
• Towards topological quantum computer
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• Differential expansion and rectangular HOMFLY for the figure eight knot
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Heisenberg algebra and a graphical calculus
• Categorification of quantum Kac-Moody superalgebras
• Checks of integrality properties in topological strings
• On possible existence of HOMFLY polynomials for virtual knots
• On matrix-model approach to simplified Khovanov-Rozansky calculus
• Logic and linear algebra: an introduction
• On ambiguity in knot polynomials for virtual knots